Hidden Digital Watermarks in Images Chiou-Ting Hsu and Ja-Ling Wu,

Hidden Digital Watermarks in Images
Chiou-Ting Hsu and Ja-Ling Wu, Senior Member, IEEE
Abstract— In this paper, an image authentication technique
by embedding digital “watermarks” into images is proposed.
Watermarking is a technique for labeling digital pictures by hiding
secret information into the images. Sophisticated watermark
embedding is a potential method to discourage unauthorized
copying or attest the origin of the images. In our approach, we
embed the watermarks with visually recognizable patterns into
the images by selectively modifying the middle-frequency parts
of the image. Several variations of the proposed method will be
addressed. The experimental results show that the proposed technique successfully survives image processing operations, image
cropping, and the Joint Photographic Experts Group (JPEG)
lossy compression.
Index Terms— Digital watermark, discrete cosine transform,
JPEG compression, pseudorandom permutation.
UE TO THE rapid and extensive growth of electronic
publishing industry, data can now be distributed much
faster and easier. Unfortunately, engineers still see immense
technical challenges in discouraging unauthorized copying and
distributing of electronic documents [1]. Conventionally, a
painting is signed by the artist to attest the copyright, an
identity card is stamped by the steel seal to avoid forgery, and
paper money is identified by the embossed portrait. Such kinds
of handwritten signatures, seals, or watermarks have been used
since ancient times as a way to identify the source or creator of
a document or picture. However, in the digital world, digital
technology for manipulating images has made it difficult to
distinguish the visual truth. “Seeing is believing” will become
an anachronism [2].
One potential solution for claiming the ownership is to
use electronic stamps or so-called watermarks, which are
embedded into the images, and have the following features:
• undeletable by hackers;
• perceptually invisible, i.e., the watermark should not
render visible artifact;
• statistically undetectable;
• resistant to lossy data compression, e.g., the Joint Photographic Experts Group (JPEG) compression;
• resistant to image manipulation and processing operations, e.g., cut-and-paste, filtering, etc.
Manuscript received August 23, 1996; revised March 6, 1998. The associate
editor coordinating the review of this manuscript and approving it for
publication was Prof. Dmitry B. Goldgof.
C.-T. Hsu is with the Communication and Multimedia Laboratory, Department of Computer Science and Information Engineering, National Taiwan
University, Taipei, Taiwan, R.O.C. (e-mail: [email protected]).
J.-L. Wu is with the Communication and Multimedia Laboratory, Department of Computer Science and Information Engineering, National Taiwan
University, Taipei, Taiwan, R.O.C. (e-mail: [email protected]).
Publisher Item Identifier S 1057-7149(99)00215-8.
In the literature, several techniques have been developed
for watermarking. In [3], three coding methods for hiding
electronic marking in document were proposed. In [4]–[7],
the watermarks are applied on the spatial domain. The major
disadvantage of spatial domain watermarking is that a common picture cropping operation may eliminate the watermark.
Other than spatial domain watermarking, frequency domain
approaches have also been proposed. In [8], a copyright
code and its random sequence of locations for embedding
are produced, and then superimposed on the image based on
a JPEG model. In [9], the spread spectrum communication
technique is also used in multimedia watermarking.
In most of the previous works [8]–[10], the watermark is a
symbol or an random number which comprises of a sequence
of bits, and can only be “detected” by employing the “detection
theory.” That is, during the verification phase, the original image is subtracted from the image in question, and the similarity
between the difference and the specific watermark is obtained.
Therefore, an experimental threshold is chosen and compared
to determine whether the image is watermarked. In this paper,
we propose a technique for embedding digital watermarks
with visually recognizable patterns into the images. Since,
in daily life, one claim a document, a creative work, and so
on, by signing one’s signature, stamping a personal seal or
an organization’s logo, such kinds of visually recognizable
patterns are more intuitive for representing one’s identity than
a sequence of random numbers is. More specifically, during the
verification phase of our work, an “extracted” visual pattern in
conjunction with the similarity measurement will be provided
for verification.
First of all, the watermark is generated as a binary pattern,
and then permuted to disperse the spatial relationship and to
increase the invisibility based on the characteristics of images.
Also, since human eyes are more sensitive to lower frequency
noise, intuitively the watermark should be embedded into
the higher frequency components to achieve better perceptual
invisibility. However, since the energy of most natural images
are concentrated on the lower frequency range, the information
hidden in the higher frequency components might be discarded
after quantization operation of lossy compression. Therefore,
to invisibly embed the watermark that can survive the lossy
data compression, a reasonable trade-off is to embed the
watermark into the middle-frequency range of the image.
In our scheme, watermarks are embedded by modifying the
middle-frequency coefficients within each image block of the
original image in considering the effect of quantization. The
experimental results show that the proposed technique could
survive several kinds of image processing and the JPEG lossy
1057–7149/99$10.00  1999 IEEE
This paper is organized as follows. The embedding approach
is described in Section II. Section III describes the watermark
extraction method. In Section IV, the experimental results are
shown. In Section V, several issues of the proposed method are
discussed. The conclusion of this paper is stated in Section VI.
In our approach, a block DCT-based algorithm is developed
to embed the image watermarking.
, and
Let be the original gray-level image of size
be a binary image of size
. In
the digital watermark
the watermark, the marked pixels are valued as one’s, and the
others are zero’s. Since only the middle-frequency range of the
host image will be processed during the watermark embedding,
is assumed to be
the resolution of a watermark image
smaller than that of the original image . For example, for
) coefficients will
each 8 8 image block, only (64
be used for the watermark embedding. The ratio of
determines the amount of information to
be embedded into the image. In general, for more robust
and invisible embedding, the amount of information can be
embedded should be reduced. On the other hand, in order
to provide a visually recognizable watermark with nontrivial
amount of information, instead of using an ID number with
trivial amount of data, making the watermark embedding
perceptually invisible is not a trivial problem.
and digital watermark
are repreThe original image
sented as
is the intensity of pixel
and is the number of bits used in each pixel.
image blocks with size 8 8. To
In , there are
of blocks as the image ,
obtain the same number
is decomposed into several blocks with size
the watermark
. For example, if
, the block size of the watermark block is 4 4,
, the block size of the
and if
watermark block is 2 2. The extra columns and rows might
be added to complete each image and watermark blocks.
the watermark to disperse its spatial relationship, i.e.,
is permuted to pixel
in a pseudoranwhere pixel
dom order.
In our approach, the permutation is implemented as follows.
. Second,
First, number each pixel from zero to
generate each number in random order. Finally, generate the
coordinate pairs by mapping the random sequence number
into a 2-D sequence. For example, for a digital watermark
128, use a “linear feedback shift register”
of size 128
[11] to generate a random sequence from 1 to 16 383. Then,
for each sequence element number , compute
as the permuted vertical and horizontal
B. Block-Based Image-Dependent Permutation
of the Watermark
In order to improve the perceptual invisibility, the characteristics of the original image should be considered, e.g., the
modifications of high frequencies or high luminance regions
are less perceptible. Such image-dependent properties can be
used to shuffle the pseudorandom permuted watermark to fit
the sensitivity of human eyes.
For each image block of size 8 8, the variances (which is
used as a measure of invisibility under watermark embedding)
are computed and sorted. For each watermark block of size,
, the amount of information (i.e.,
the number of signed pixels) are sorted also. Then, shuffle
each watermark block into the spatial position according the
corresponding sorting order of the image block, i.e.,
; in which
A. Pseudorandom Permutation of the Watermark
In the approach, each watermark block is embedded into
the middle-frequency range of each image block using blocktransform instead of full-frame transform. Therefore, each
watermark block will only be dispersed over its corresponding
image block, instead of the entire spatial image. Obviously,
without appropriate adjustment for the spatial relationship of
the watermark, a common picture-cropping operation may
eliminate the watermark.
To survive picture-cropping, a fast two-dimensional (2-D)
pseudorandom number traversing method is used to permute
is shuffled to block
by the blockwhere block
based permutation. Fig. 1 shows an example of the sorting
and the permutation.
Fig. 1. Example of block-based image-dependent permutation, where for
each 8
8 image block, the variance is computed and sorted, and for each
watermark block of size ( 1 N8 ) ( 2 N8 ), the amount of information
(i.e., the number of signed pixels) is sorted also, and then each watermark
block is shuffled into the spatial position according the corresponding sorting
order of the image.
M2 2M2
Fig. 2. Example of defining the middle-frequency coefficients, in which the
coefficients are picked up in zigzag-scan order and then reordered into block
of 4
4. (a) Zigzag ordering of DCT coefficients and the middle frequency
coefficients are shown in the shadow area. (b) Picked up coefficients are
4 block.
mapped into the 4
C. Block Transformation of the Image
Since the discrete cosine transform (DCT) used by JPEG
8, the input image
[12] is performed on blocks of 8
is divided into blocks of 8
8, and each block is DCT
transformed independently. That is,
M 2
M 2
Fig. 3. Residual mask, where each square includes a reduced image block
of size ( 1
N ) ( 2 N ), and position stands for the current
reduced block.
where FDCT denotes the operation of forward DCT.
D. Choice of Middle-Frequency Coefficients
The human eye is more sensitive to noise in lower frequency
components than in higher frequency ones. However, the
energy of most natural images are concentrated in the lower
frequency range, and the information hidden in the higher
frequency components might be discarded after quantization
operation of lossy compression. In order to invisibly embed
the watermark that can survive lossy data compressions, a
reasonable trade-off is to embed the watermark into the
middle-frequency range of the image. To this end, for each
) coefficients are selected
8 8 image block, only (64
out of the 64 DCT coefficients. Those selected coefficients are
then mapped into a reduced image block of size
. That is, the middle-frequency coefficients selected
are collected to compose
from the image of size
, which has the same
a reduced image of size
resolution with the binary watermark.
Fig. 4. Luminance quantization table. (a) Default JPEG quantization table.
(b) JPEG quantization table used by Image Alchemy, Handmade Software Inc.
For example, if
, only 16 DCT
coefficients are processed during the watermark embedding,
and the other 48 DCT coefficients are left unchanged. Fig. 2
exemplifies our definition of the middle-frequency coefficients,
which are mapped into a reduced block of size 4 4.
E. Modification of the DCT Coefficients
Now, a permuted digital watermark and a reduced image
(which contains only the middle-frequency components of the
are obtained. For
original image) both with size
, the
each watermark block of size
at the
reduced image block of size
corresponding spatial position will be modified adequately to
embed the watermarked pixels.
In our opinion, embedding each watermarked pixel by
modifying the polarity between the corresponding pixels in
neighboring blocks is an effective approach to achieve the
invisibility and survival for low compression ratio of JPEG.
However, this method is not robust with respect to the com. At part
pression attacks with higher compression ratio
(a), we will address the technical challenges. At part (b), an
Fig. 5.
Watermark embedding steps.
improved method that is resistant to higher compression ratio
will be described.
1) Embedding into the Relationship Between Neighboring
Blocks: A 2-D residual mask is used to compute the polarity
of the chosen middle-frequency coefficients between neighboring blocks. For example, in Fig. 3, if
, then the polarity is a binary pattern (zero
or one) which represents the coefficients at the position of
or less
the current reduced-block is larger polarity
than the coefficient at the corresponding
position of the previous reduced-block. That is,
Fig. 6. Watermark extracting steps.
polarity. That is,
After the binary polarity pattern is obtained, for each marked
pixel of the permuted watermark, modify the DCT coefficients
according the residual mask to reverse the corresponding
from such that the differences between
Then, construct
are minimized or smaller than a user specified
based on poNote that the “Expand” operation constructs
larity . For example, assign the initial coefficient
, and add (or subtract) the coefficients of neighboring
blocks according to the residual mask in order to match the
. Then, proceed to successive
corresponding polarity
coefficients by modifying only those who will not affect the
polarities of the previous-processed coefficients.
In order to improve the invisibility, the polarity should be
computed for absolute value of the coefficients so that the
sign (plus and minus signs) of the coefficients are hopefully
preserved to reduce the changes introduced by modification.
Besides, in order to survive the JPEG lossy compression, the
quantization effect utilized in the JPEG codec must be considered. Fig. 4(a) shows the suggested luminance quantization
table for JPEG standard, which usually cause perceptible artifacts when viewed on high-quality displays. Fig. 4(b) shows
another quantization table used in most JPEG software. The
values are almost half of the corresponding JPEG suggested
quantization values. Based on a referenced quantization table,
the polarity are computed from coefficients after quantization
and then dequantization. Therefore, in case of quantization
attack, the correct marked pixel should be extracted. That is,
the polarity should be
Fig. 7. Example of the proposed watermarking approach. (a) Test image
40.83 dB). (d)
Lena. (b) Watermark. (c) Watermarked image (with PSNR
Extracted watermark (with NC = 1).
relatively more reliable DC coefficient (instead of the middlefrequency coefficients of neighboring blocks) is used as a
reference value for each block. That is,
is the quantization value at the corresponding
However, since quantization tends to make many coefficients zero (especially those for higher spatial frequencies),
if the modification of the coefficients is not large enough,
most middle-frequency coefficients will also be truncated to
zero after coarse quantization. Besides, in order to preserve
the polarity to survive quantization according the specified
residual mask, not only those middle-frequency coefficients
in the current block have to be modified, but also all the
neighboring blocks involved in the residual mask have be to
modified with the same volume. Therefore, although survival
for lossy compression, the watermarked image which are
embedded with large modification will not be perceptually
equivalent to the original image.
2) Embedding into the Relationship Within Each Block In
order to overcome the technical challenges addressed above,
while still hopefully not to propagate the modifications into
the neighboring blocks (so as to improve the invisibility), the
For each marked pixel, add (or subtract) the corresponding
will have the
coefficient so that the modified coefficients
reverse polarity .
F. Inverse Block Transform
Finally, map the modified middle-frequency coefficients
into to get . Then, inverse DCT (IDCT) of the associated
Fig. 8. Another example of the proposed approach. (a) Cameraman test image. (b) Watermarked image (with PSNR
= 39.29 dB).
result to obtained the embedded image.
Fig. 5 illustrates the steps of embedding the watermark, where
256, and a
Lena is used as the test image of size 256
seal with Chiou-Ting Hsu’s Chinese name is used as a binary
watermark of size 128
The extraction of watermark requires the original image,
the watermarked image, and either the watermark or the
permutation mapping used in image-dependent permutation
during the embedding steps. The extraction steps are described
as follows.
Fig. 9. (a) Blurred version of Fig. 7(c). (b) Extracted watermark with
NC = 0:982.
A. Block Transformation
Perform exclusive-or (XOR) operation on these two polarity
patterns to obtain a permuted binary data, i.e.,
Both the original image
DCT transformed.
and the image in question
C. Extract the Permuted Data
D. Reverse Block-Based Image-Dependent Permutation
B. Generation of Polarity Patterns
Generate the reduced images which contain only the middlefrequency coefficients and then use these middle-frequency
DCT coefficients to produce the polarity patterns. That is,
The image-dependent permutation mapping could be obtained either by saving as a file during the embedding steps or
recomputed from the original image and the watermark. Based
to get
on the mapping, reverse permute
E. Reverse Pseudorandom Permutation
to get the watermark
and then
is reverse-permuted to
predefined pseudorandom order.
according to the
Fig. 10. (a) Image enhanced version of Fig. 7(c) with slightly enhanced
contrast. (b) Extracted watermark with NC = 0:9985.
Fig. 12. (a) Quarter of an embedded image is discarded. And (b)–(d) are the
extracted watermarks, where (b) is without pseudorandom permutation nor
block-based image-dependent permutation (NC = 0:7922), (c) is with only
block based permutation (NC = 0:9372), and (d) is with both permutations
(NC = 0:7623).
Fig. 11. (a) Image enhanced version of Fig. 7(c) with strongly enhanced
contrast. (b) Extracted watermark with NC = 0:973.
F. Similarity Measurement
In our scheme, the extracted watermark is a visually recognizable pattern. The viewer can compare the results with the
referenced watermark subjectively. However, the subjective
measurement is dependent on factors such as the expertise
of the viewers, the experimental conditions, etc. Therefore,
a quantitative measurement is needed to provide objective
judgment of the extracting fidelity. We define the similarand
ity measurement between the referenced watermark
extracted watermark
Normalized Correlation
which is the cross-correlation normalized by the reference
watermark energy to give unity as the peak correlation.
Fig. 6 illustrates the procedures for extracting the watermarks.
Fig. 13.
Relationship between the cropping ratios and the NC values.
A. Image Processing Operation
Smoothing operations are used to diminish spurious effects
which may be present in images from a poor transmission
channel. Fig. 9 shows a blurred version of the watermarked
image, and the extracted watermark, though interfered by noise
is still recognizable.
The contrast of an image is usually adjusted to enhance the
subjective quality. Figs. 10 and 11 show the results of applying
slightly and strongly enhanced operations to a watermarked
image accordingly. The extracted results are still highly similar
to the original watermark.
Fig. 7 shows an example of embedding and extracting
results, where Lena is used as the test image again, and a
pattern with “NTU CSIE CMLAB” is used as the watermark.
Fig. 8 is another example, where the cameraman image is
watermarked with Fig. 7(b).
B. Image Cropping Operation
During the image manipulation, the uninterested part of
an image is usually cropped. As described in Section II-A, a
pseudorandom permutation is performed to disperse the spatial
relationship of the watermark. Therefore, it would be hard for
Fig. 14. Extracted watermarks of the cropped versions of Fig. 7(c). (a) A quarter of the image is cropped, and the missing portions is filled with zero
values (NC = 0:7623). (b) A quarter of the image is cropped, and the missing portion is filled with unwatermarked image (NC = 0:7339). (c)
Half of the image is cropped, and the missing portions is filled with zero values (NC = 0:5964). (d) Half of the image is cropped, and the missing
portions is filled with unwatermarked image (NC = 0:5276).
Fig. 15. Extracted watermarks of JPEG compressed version of Fig. 7(c), where (a) with compression ratio 5.92 and NC = 0:99, (b) with compression ratio
7.16 and NC = 0:883, (c) with compression ratio 8.46 and NC = 0:726, and (d) with compression ratio 9.05 and NC = 0:661.
a “pirate” to detect or remove the watermark by cutting some
part of the image. For example, in Fig. 12(a), a quarter of
the watermarked image is discarded. If neither pseudorandom
nor block-based image dependent permutation was applied
during the embedding, the extracted watermark [as shown in
Fig. 12(b)] will reveal the spatial information of the watermark
embedding. However, once the permutation is introduced, the
lost information will be distributed over the whole image, and
the extracted error will also be distributed over the whole
result. In such case, the results will be interfered with noises
but will not reveal the spatial position of the watermark [as
shown in Fig. 12(c) and (d)] Note that, since Fig. 12(c) is
without using the pseudorandom permutation, the noises are
less random then 12(d) does.
Fig. 13 shows the relationship between the similarity measurement NC and the cropping ratio. Since a pseudorandom
permutation is applied, the effect of cropping operation to the
NC of the extracted results is almost linear.
Fig. 14 shows the extracted results from various cropped
image. Fig. 14(a) and (c) are extracted from cropped images
where the missing portions are filled with zero values, and
Fig. 14(b) and (d) are extracted from cropped images where
the missing portions are filled with original unwatermarked
images. As shown in the figure, filling with zero values in the
missing portions distributes more noises over the entire results
and influences the visual recognition.
Fig. 16. If M1 = N1 =4 and M2 = N2 =4, then there are only four
middle-frequency coefficients should be chosen for each watermark. These
three watermarks would be embedded into one image with their individual
user key, or identical watermark could be repeatedly embedded three times
to improve the robustness.
C. JPEG Lossy Compression
Fig. 15 shows the extracted results from JPEG compressed
version of the watermarked images with compression ratio
5.92, 7.16, 8.46, and 9.05. The quantization table in Fig. 4(a)
is used as the referenced quantization values as described
in Section II-E. Table I shows that as the compression ratio
increases, the NC value decrease accordingly. Therefore, as
the compression ratio are high enough to quantize DCT
coefficients very coarsely, the watermark will be destroyed and
128 as shown in (a), (b), and (c) as watermarks 1–3 of Fig. 16
Fig. 17. Example of multiple watermarking using three watermarks with size 128
39.48 dB.
accordingly, where (d) is the host image with size of 512
512, and (e) is the multiple-watermarked image with PSNR
become indiscernible. However, in this situation, the quality
of the JPEG compressed image (without being watermarked)
will be degraded severely so that the processes of digital
watermarking become less meaningful.
A block DCT-based watermarking technique for images is
proposed in this work. There are some issues are worthy of
giving further discussion as follows.
A. Image Dependent Permutation
In Section II-B, a block-based image-dependent permutation according to the characteristics of both the image and
watermark is used in our work. Although the watermark is
embedded into the middle-frequency coefficients, for those
blocks with little variances (i.e., the blocks containing low
frequency contents), the modification of DCT coefficients will
introduce visible artifacts. To reduce the artifacts, we sort
the variances of image blocks and the amount of information
within each watermark block, and then map the watermark
blocks with more signed pixels into those image blocks with
higher variances.
However, based on our simulation, no gain of objective
quality (such as PSNR) can be obtained by using these kinds
of permutations. However, better subjective quality, especially
for those smoother parts of the image, could be obtained.
B. User Key
A “user key” is provided as a secret key that can be
used to serve various embedding processes by using the
same embedding technology. Besides, a user key is treated
as a parameter during the extracting steps. In the proposed
embedding method, a “user key” should defines the following
1) Seed of the pseudorandom number generator:
The seed defines the initial position of an pseudorandom
permutation, which could be any one between one and
2) Choice of middle-frequency coefficients:
middle-frequency coefficients
There are
should be picked out in all of 64 DCT coefficients
for each block. In the user key, the coefficients to be
processed should be specified.
3) Mapping of the chosen coefficients into a reduced block:
Fig. 2(b) shows one way to map the chosen coefficients.
Other kinds of mapping are also possible.
C. Size of Watermarks
With visually recognizable watermarks, there are nontrivial
amount of information will be embedded into the original
image. Obviously, once the ratio of
becomes larger, the number of DCT coefficients involved
in the embedding will be smaller. In such case, the invisibility will be improved. In addition, multiple watermarking
or repeatedly embedding identical watermarks to harden the
robustness is also possible. For example, if
, then there are only four middle-frequency
coefficients should be chosen from 64 coefficients for the
watermark. As shown in Fig. 16, three watermarks could be
embedded into an image with different user key which chooses
different coefficients from the image block. Fig. 17 shows an
Fig. 18. Extracted watermarks from JPEG compressed version of Fig. 17(e)
with individual user keys, where (a) with compression ratio 5.58 and NC
values are 0.996, 0.993 and 0.975 accordingly, and (b) with compression
ratio 7.13 and NC values are 0.995, 0.983, and 0.892 accordingly.
example of multiple watermarked result from Fig. 16, and
Fig. 18 shows the extracted results from JPEG compressed
image of Fig. 17(e) with different user key.
This paper has presented a technique for embedding digital
watermark into the images. The embedding and extracting
methods of the DCT-based approach have been described.
The experimental results show the proposed embedding
technique can survive the cropping of an image, image enhancement and the JPEG lossy compression. By carefully
defining the “user key,” multiple watermarking and repeatedly embedding to harden the robustness are available. Our
technique could also be applied to the multiresolution image
structures with some modification about the choice of middlefrequency coefficients [13].
Other kinds of attacks, such as image resampling and image
rotation, are still challenging to our current work, and have
been chosen to be the major direction of our future work.
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Chiou-Ting Hsu received the B.S. degree in
computer and information science from National
Chiao Tung University, Hsin-Chu, Taiwan, R.O.C.,
in 1991, and the Ph.D. degree in computer science
and information engineering from National Taiwan
University (NTU), Taipei, Taiwan, in 1997.
She is currently a Post-doctoral Researcher with
the Communication and Multimedia Laboratory,
Department of Computer Science and Information
Engineering, NTU. Her research interests are
in digital watermarking, multiresolution signal
processing, and image/video coding.
Ja-Ling Wu (S’85–A’87–SM’98) was born in
Taipei, Taiwan, on November 24, 1956. He received
the B.S. degree in electronics engineering from
Tam-Kang University, Tam-Shoei, Taiwan, R.O.C.,
in 1979, and the M.S. and Ph.D. degrees in electrical
engineering from Tatung Institute of Technology,
Taipei, in 1981 and 1986, respectively.
From August 1986 to July 1987, he was an
Associate Professor in the Department of Electrical
Engineering, Tatung Institute of Technology. He
became an Associate Professor at the Department of
Computer Science and Information Engineering, National Taiwan University,
Taipei, in August 1987, and a Professor in August 1990. Since August 1996,
he has been with National Chi-Nan University, Puli, Taiwan, as the Chairman
of the Department of Information Engineering. He currently teaches courses
in digital signal processing and multimedia data compression and conducts
research in the areas of signal processing, image/video coding, and digital
watermarking techniques. He has authored more than 150 technical papers
in these areas.
Dr. Wu received the Outstanding Research Award of the National Science
Council of the Republic of China from 1987 to 1994, the Outstanding
Youth Medal of the Republic of China in 1989, the Award for 1993 R.O.C.
Distinguished Information People of the Year, the Special Long-Term Award
for Collaboratory Research, sponsored by the Acer Corporation in 1994,
the Best Paper Award for the R.O.C. Association of Image Processing
and Multimedia Applications in 1995, and the Long-Term Medal for Ten
Distinguished Researchers in 1996.